So my idea is halfway between the two: place a large, weighted concrete cylinder with no end caps above the hole - a hollow top hat, if you like. It needs to be big, like 25' x 25' or larger; height is more important than diameter. This in itself does nothing to stem the flow - but nor does it obstruct it. So the cylinder can then be sealed around the bottom and fixed to the seabed without interference from the pressure of the outrushing oil.
Then one can begin filling the cylinder with gravel or whatever is suitable - smallest material first, working up to rocks. As we begin covering the gusher, the pressure will obviously push some of the filler material out of the way...but as it's inside a cylinder, the filler is just going to get pushed against the side of the cylinder, where its weight is going to increase the downward pressure on the material at the bottom, which has nowhere to go except in towards the center. When the aggregate pressure at the bottom of the cylinder from the sides into the center exceeds the pressure of the oil, it will pinch off the flow, like a valve. This of course assumes perfect packing of the filler material; in reality the oil will diffuse through it, but in doing so the pressure will be distributed across the diameter of the cylinder, which will make it much easier to cap.
Or we could just go with Andy Borowitz's suggestion to plug the whole with BP executives....